Restarting Conjugate Gradient Methods for Nonsymmetric Linear Equations

重新启动是减少数据的存储和正交化成本的一种方式。 非对称线性方程组的共轭梯度法 方程 然而，重新启动减慢了收敛。 在 Arnoldi和GMRES版本的共轭梯度法， 可以解决相关的特征值问题。 本次调查使用 特征值问题，以保留一些信息中丢失的 重新启动，从而改善线性方程组的收敛性 解决方法 这是通过添加几个近似特征向量来完成的 线性方程组的子空间。 一些初步的实验表明，该方法可以非常 有效 需要测试和理论研究来确定 该方法在不同类型的矩阵上的效果如何。 更 还需要进行研究，以确定最佳的执行办法。

Restarting is one way to reduce storage and orthogonalization costs of conjugate gradient methods for large systems of nonsymmetric linear equations. However, restarting slows down the convergence. In the Arnoldi and GMRES versions of the conjugate gradient method, the associated eigenvalue problem can be solved. This investigation uses the eigenvalue problem to retain some of the information lost in the restart and thus improve the convergence of the linear equations solution method. This is done by adding a few approximate eigenvectors to the subspace that is used for the linear equations problem. Some preliminary experimentation show that the method can be very effective. Testing and theoretical research are needed to determine how well the method works with different types of matrices. More research is also needed to determine the best implementation.